RATIONAL CURVES ON CUBIC HYPERSURFACES OVER FINITE FIELDS

Mathematika, vol. 67, pp. 366–387

Abstract

Given a smooth cubic hypersurface $X$ over a finite field of characteristic greater than 3 and two generic points on $X$, we use a function field analogue of the Hardy-Littlewood circle method to obtain an asymptotic formula for the number of degree $d$ rational curves on $X$ passing through those two points. We use this to deduce the dimension and irreducibility of the moduli space parametrising such curves, for large enough $d$.

Authors 1

1. Adelina Mânzăţeanu corresponding Aachen

   Leiden University

   Affiliation as printed

   Mathematisch Instituut Leiden University Niels Bohrweg 1, 2333 CA Leiden The Netherlands

   Mathematisch Instituut Leiden University Niels Bohrweg 1 2333 CA Leiden, the Netherlands